Combinatorics and Optimization: Recent submissions
Now showing items 120 of 417

Algorithmic and Linear ProgrammingBased Techniques for the Maximum Utility Problem
(University of Waterloo, 20230525)A common topic of study in the subfield of Operations Research known as Revenue Management is finding optimal prices for a line of products given customer preferences. While there exists a large number of ways to model ... 
LowRank Plus Sparse Decompositions of LargeScale Matrices via Semidefinite Optimization
(University of Waterloo, 20230519)We study the problem of decomposing a symmetric matrix into the sum of a lowrank symmetric positive semidefinite matrix and a tridiagonal matrix, and a relaxation which looks for symmetric positive semidefinite matrices ... 
Graph Coverings with Few Eigenvalues or No Short Cycles
(University of Waterloo, 20230518)This thesis addresses the extent of the covering graph construction. How much must a cover X resemble the graph Y that it covers? How much can X deviate from Y? The main statistics of X and Y which we will measure are their ... 
Nearoptimal quantum strategies for nonlocal games, approximate representations, and BCS algebras
(University of Waterloo, 20230504)Quantum correlations can be viewed as particular abstract states on the tensor product of operator systems which model quantum measurement scenarios. In the paradigm of nonlocal games, this perspective illustrates a ... 
NonAdaptive Matroid Prophet Inequalities
(University of Waterloo, 20230504)We consider the problem of matroid prophet inequalities. This problem has been ex tensively studied in case of adaptive prices, with [KW12] obtaining a tight 2competitive mechanism for all the matroids. However, the ... 
Semidefinite Programming Relaxations of the Simplified Wasserstein Barycenter Problem: An ADMM Approach
(University of Waterloo, 20230504)The Simplified Wasserstein Barycenter problem, the problem of picking k points each chosen from a distinct set of n points as to minimize the sum of distances to their barycenter, finds applications in various areas of ... 
Dynamic Pricing Schemes in Combinatorial Markets
(University of Waterloo, 20230501)In combinatorial markets where buyers are selfinterested, the buyers may make purchases that lead to suboptimal item allocations. As a central coordinator, our goal is to impose prices on the items of the market so that ... 
Algorithms for Analytic Combinatorics in Several Variables
(University of Waterloo, 20230425)Given a multivariate rational generating function we are interested in computing asymptotic formulas for the sequences encoded by the coefficients. In this thesis we apply the theory of analytic combinatorics in several ... 
On coloring digraphs with forbidden induced subgraphs
(University of Waterloo, 20230425)This thesis mainly focuses on the structural properties of digraphs with high dichromatic number. The dichromatic number of a digraph $D$, denoted by $\dichi(D)$, is designed to be the directed analog of the chromatic ... 
Analyzing Tree Attachments in 2CrossingCritical Graphs with a V8 Minor
(University of Waterloo, 20230425)The crossing number of a graph is the minimum number of pairwise edge crossings in a drawing of the graph in the plane. A graph G is kcrossingcritical if its crossing number is at least k and if every proper subgraph H ... 
PostQuantum Account Recovery for Passwordless Authentication
(University of Waterloo, 20230424)WebAuthn is a passwordless authentication protocol which allows users to authenticate to online services using publickey cryptography. Users prove their identity based on possession of a private key, which is stored on a ... 
Implicit Loss of Surjectivity and Facial Reduction: Theory and Applications
(University of Waterloo, 20230309)Facial reduction, pioneered by Borwein and Wolkowicz, is a preprocessing method that is commonly used to obtain strict feasibility in the reformulated, reduced constraint system. The importance of strict feasibility is ... 
The EdmondsGiles Conjecture and its Relaxations
(University of Waterloo, 20221223)Given a directed graph, a directed cut is a cut with all arcs oriented in the same direction, and a directed join is a set of arcs which intersects every directed cut at least once. Edmonds and Giles conjectured for all ... 
kConnectedness and kFactors in the SemiRandom Graph Process
(University of Waterloo, 20221220)The semirandom graph process is a singleplayer graph game where the player is initially presented an edgeless graph with n vertices. In each round, the player is offered a vertex u uniformly at random and subsequently ... 
Mixed Integer Programming Approaches for Group Decision Making
(University of Waterloo, 20221026)Group decision making problems are everywhere in our daytoday lives and have great influence on the daily operation of companies and institutions. With the recent advances in computational technology, it's not surprising ... 
Aspects of Quantum Field Theory in Enumerative Graph Theory
(University of Waterloo, 20221024)While a quantum field theorist has many uses for mathematics of all kinds, the relationship between quantum field theory and mathematics is far too fluid in the world of modern research to be described as the simple provision ... 
Digraphs with All Induced Directed Cycles of the Same Length are not → χ Bounded
(20221007)For t > 2, let us call a digraph D tchordal if all induced directed cycles in D have length equal to t. In an earlier paper, we asked for which t it is true that tchordal graphs with bounded clique number have bounded ... 
Enumerative perspectives on chord diagrams
(University of Waterloo, 20221007)The topic of this thesis is enumerating certain classes of chord diagrams, perfect matchings of the interval $\{1, 2, \ldots, 2n\}$. We consider hereditary classes of chord diagrams that are restricted to satisfy one of ... 
Edgedisjoint Linkages in Infinite Graphs
(University of Waterloo, 20220926)The main subject of this thesis is the infinite graph version of the weak linkage conjecture by Thomassen [24]. We first prove results about the structure of the lifting graph; Theorems 2.2.8, 2.2.24, and 2.3.1. As an ... 
Clique minors in dense matroids
(University of Waterloo, 20220923)The objective of this thesis is to bound the number of points a $U_{2,\ell+2}$ and $M(K_{k+1})$minorfree matroid has. We first prove that a sufficiently large matroid will contain a structure called a tower. We then use ...